Cohorts of 3-6 patients receive escalating doses of capecitabine until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity (DLT). The recommended phase II dose is defined as the dose preceding the MTD, provided no more than 3 of 12 patients experience DLT at that dose. Twenty additional patients with cancer of the upper gastrointestinal tract receive treatment with cisplatin and capecitabine at the recommended phase II dose for at least 6 months in the absence of disease progression or unacceptable toxicity.